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X Question 5 0/8 pts 9 1 98 0 Details Score on last try: 0 of 8 pts. See Details for more. Get a similar question You can retry this question below Find an interval around x = 0 for which the given initial-value problem has a unique solution. (a - 16)y"' + 10y = x y(0) = 0 and y' (0) = 1 Interval (enter your answer using interval notation): 08 ( - 00, 16) Show Detailed Solution This is second order linear differential equation of the form a2(x)y"+ al(x)y + ao(x) = g(x) and a unique solution exists where ai (a) is continuous, g(x) is continuous, and a2(x) # 0 a2 (2) = x- 16 a1 (2) = 0 ao (2) = 10 g(2 ) = x These functions are continuous on ( - co, co) a2(2) = x - 16 0, when x * 16 Thus, a unique solution will exist on the intervals ( - oo, 16) U (16, co) Around x = 0 the interval where a unique solution exists is ( - 0o, 16)